Block #947,593

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/22/2015, 3:07:33 PM · Difficulty 10.8987 · 5,866,583 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

c728fdb64e4afc6519fdbcec4aaad76bebf965a2248d5dfd820a45fa142ae524

View on Chainz ↗

Height

#947,593

Difficulty

10.898709

Transactions

Size

1.15 KB

Version

Bits

0ae611d2

Nonce

118,911,026

Timestamp

2/22/2015, 3:07:33 PM

Confirmations

5,866,583

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

57459a96c7813c8f34bc6c60e74992462412e8f9c93355fdba65eaa7cdaaba56

Transactions (4)

Coinbased064bfa18a30fa…bbd609a03f022e

1 in → 1 out8.4400 XPM116 B

ANSXnLY2…Sd25TjkD

d1048cd510d514…ed2f3d203fd050

3 in → 2 out214.4245 XPM521 B

AHqAhJKY…jC8vs5ud AQ5cRuWn…ajoU8war

64465e0f14511a…cb0a551134a400

1 in → 2 out4.7954 XPM226 B

Addmk7ub…896mnUY8 AHRoBSh4…BSVTQ36Q

c8261e96760e2f…2386fe44a4ac10

1 in → 2 out1.3765 XPM226 B

AeednALq…tXB7tBN2 AP4BUBdX…xZ92AHh8

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.553 × 10⁹⁷(98-digit number)

35538054089982389126…11762131080544061439

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

3.553 × 10⁹⁷(98-digit number)

35538054089982389126…11762131080544061439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.553 × 10⁹⁷(98-digit number)

35538054089982389126…11762131080544061441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

7.107 × 10⁹⁷(98-digit number)

71076108179964778253…23524262161088122879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.107 × 10⁹⁷(98-digit number)

71076108179964778253…23524262161088122881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.421 × 10⁹⁸(99-digit number)

14215221635992955650…47048524322176245759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.421 × 10⁹⁸(99-digit number)

14215221635992955650…47048524322176245761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.843 × 10⁹⁸(99-digit number)

28430443271985911301…94097048644352491519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.843 × 10⁹⁸(99-digit number)

28430443271985911301…94097048644352491521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

5.686 × 10⁹⁸(99-digit number)

56860886543971822602…88194097288704983039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.686 × 10⁹⁸(99-digit number)

56860886543971822602…88194097288704983041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #947,593

Cookie Preferences